In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, a dispersive partial differential equation or dispersive PDE is a
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
The function is often thought of as an "unknown" that solves the equation, similar to ho ...
that is
dispersive. In this context, dispersion means that waves of different
wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats.
In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
propagate at different
phase velocities.
Examples
Linear equations
*
Euler–Bernoulli beam equation with time-dependent loading
*Airy equation
*
Schrödinger equation
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...
*
Klein–Gordon equation
Nonlinear equations
*
nonlinear Schrödinger equation
In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. It is a classical field equation whose principal applications are to the propagation of light in nonli ...
*
Korteweg–de Vries equation (or KdV equation)
*
Boussinesq equation (water waves)
*
sine–Gordon equation
See also
*
Dispersion (optics)
Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Sometimes the term chromatic dispersion is used to refer to optics specifically, as opposed to wave propagation in general. A medium having this common ...
*
Dispersion (water waves)
*
Dispersionless equation
References
*
External links
*Th
Dispersive PDE Wiki
{{mathanalysis-stub
Partial differential equations
Nonlinear systems